Using New Outlook on Windows for professional communication and productivity
If you want to directly import contact from New Outlook to Classic Outlook, you can refer to the AI answer for manual method to export .csv file. Import or export contacts in Outlook using a .csv file
Additionally, what type of account are you using in Outlook (Microsoft 365/Exchange, POP/IMAP, etc.)?
Normally, if the contacts are stored on the mail server (for example, Microsoft 365/Exchange or Outlook.com), the contacts should automatically sync across both New Outlook and Outlook Classic when the same account is added.
Also, I want to let you know in New Outlook, you can go to View and there will be a sync option.